论文标题
非本地分支马尔可夫过程的次数很多
Many-to-few for non-local branching Markov process
论文作者
论文摘要
我们在非本地分支马尔可夫流程的一般环境中提供了多个公式的公式。该公式允许一个人在不同时间计算对种群功能的K折总和的期望。结果[11]和[8]中引入的结果将结果[14]概括为非本地设置。作为应用程序，我们考虑了分支过程至关重要的情况，并有条件在很大程度上生存。在这种情况下，我们证明了一个通用公式，用于在两个不同时间从人群中统一选择的两个粒子的死亡时间的限制定律，因为T倾向于无穷大。此外，我们在两个不同时间（在同一渐近状态下）描述了人口规模的限制定律。
We provide a many-to-few formula in the general setting of non-local branching Markov processes. This formula allows one to compute expectations of k-fold sums over functions of the population at k different times. The result generalises [14] to the non-local setting, as introduced in [11] and [8]. As an application, we consider the case when the branching process is critical, and conditioned to survive for a large time. In this setting, we prove a general formula for the limiting law of the death time of the most recent common ancestor of two particles selected uniformly from the population at two different times, as t tends to infinity. Moreover, we describe the limiting law of the population sizes at two different times, in the same asymptotic regime.
